What is the Pythagorean triplet, whose largest member is 65?

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16, 63, 64

18, 63, 66

18, 63, 64

16, 63, 66

answer is A.

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Detailed Solution

It is required to find the Pythagorean triplet, whose largest member is 65.
A Pythagorean triplet is a set of three numbers where the squares of the smaller two numbers added together equal the square of the largest.
For a natural number m > 1,

2 m 2 + (m 2 − 1) 2 = (m 2 + 1) 2

So,

2 m, m 2 − 1, m 2 + 1

form Pythagorean triplet.
Calculate the value of m.
The largest member = 65.

⇒ m 2 + 1 = 65 ⇒ m 2 = 64 ⇒ m = 8

Find the other numbers,

⇒ 2m = 2 × 8 = 16 ⇒ m 2 − 1 = 82 − 1 ⇒ 64 − 1 = 63

Hence the required triplet is (16, 63, 64), whose largest member is 65.
Therefore, option 1 is correct.

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